is a new employer liable to be sued by former employer in a non compete?

Left former employer, thought the non compete was void due to old employer shook hands, wished me well, and knew I was going to work for small competitor. 6 months later, old employer sent new employer a copy of non compete agreement, never threatened legal action, nor was legal action ever taken. 3 months later I was told I was being laid off for lack of work. after collecting unemployment for a while, new employer challenged unemployment. Had a hearing with unemployment, was denied unemployment stating new employer discharged me to avoid legal liability. Took case to civil court, judge ruled in favor of unemployments decision. My question, if the new employer, and myself, were unaware of existing non compete, could the new employer be at risk for legal liability, since evidently the contract was between myself and the former employer, not my new employer? Please provide ohio law that covers this. I still do not feel I was discharged in connection with work. I have one appeal left. Thank You!!!